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sin^2 0+sin^2 1+sin^2 2....sin^2 90

 Apr 20, 2015

Best Answer 

 #1
avatar+99356 
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$$\\sin^2 0+sin^2 1+sin^2 2....sin^2 90\\\\
=[sin^2 0+sin^2 1+...sin^244]\;\;\;+\;\;\;sin^245\;\;[+sin^246+....sin^2 90]\\\\
=(sin^2 0+sin^2 90)+....(sin^244+sin^246)+sin^245 \\\\
=(sin^2 0+cos^20)+....(sin^244+cos^244)\;\;+sin^245 \\\\
=(1)+....(1)\;\;+sin^245 \\\\
=45+sin^245\\\\
=45+(\frac{1}{\sqrt2})^2\\\\
=45\frac{1}{2}\\\\$$

.
 Apr 20, 2015
 #1
avatar+99356 
+8
Best Answer

$$\\sin^2 0+sin^2 1+sin^2 2....sin^2 90\\\\
=[sin^2 0+sin^2 1+...sin^244]\;\;\;+\;\;\;sin^245\;\;[+sin^246+....sin^2 90]\\\\
=(sin^2 0+sin^2 90)+....(sin^244+sin^246)+sin^245 \\\\
=(sin^2 0+cos^20)+....(sin^244+cos^244)\;\;+sin^245 \\\\
=(1)+....(1)\;\;+sin^245 \\\\
=45+sin^245\\\\
=45+(\frac{1}{\sqrt2})^2\\\\
=45\frac{1}{2}\\\\$$

Melody Apr 20, 2015

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